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Percolation on Finite Cayley Graphs
Published online by Cambridge University Press: 07 June 2006
Abstract
In this paper, we study percolation on finite Cayley graphs. A conjecture of Benjamini says that the critical percolation $p_c$ of any vertex-transitive graph satisfying a certain diameter condition can be bounded away from one. We prove Benjamini's conjecture for some special classes of Cayley graphs. We also establish a reduction theorem, which allows us to build Cayley graphs for large groups without increasing $p_c$.
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- 2006 Cambridge University Press
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